We continued our research of three cortical reflexes that Dr. Miless laboratory discovered in the 80s and 90s that are important for the visual stabilization of gaze in 3D. Most recently we concentrated our efforts on one of them, the one that uses binocular disparity to generate horizontal and vertical vergence eye movements to eliminate fixation disparities (Disparity Vergence Response, DVR). We recorded the initial disparity vergence responses (DVRs) elicited by 1-D sinusoidal gratings differing in phase at the two eyes by wavelength and defined by luminance modulation (LM) or contrast modulation (CM) of dynamic binary noise. Both LM and CM stimuli elicited DVRs, but those to CM had longer latency (on average by 20 ms). DVRs showed sigmoidal dependence on depth of modulation, with higher thresholds for CM than for LM. With both LM and CM stimuli, fixing the modulation at one eye well above threshold rendered the DVR hypersensitive to low-level modulation at the other eye (dichoptic facilitation). Disparities defined by LM at one eye and CM at the other generated weak DVRs in the wrong direction, consistent with mediation entirely by distortion products associated with the CM stimulus. These (reversed) DVRs could be nulled by adding LM to the CM stimulus (in-phase), and the greater the depth of the CM, the greater the added LM required for nulling, exactly as predicted by a simple compressive non-linearity. We conclude that disparities defined by LM and by CM are sensed by independent cortical mechanisms, at least for the purposes of generating short-latency vergence eye movements to disparity steps.